/// \file
/// \ingroup tutorial_math
/// \notebook
/// Example macro describing the student t distribution
///
/// ~~~{.cpp}
/// root[0]: .x tStudent.C
/// ~~~
///
/// It draws the pdf, the cdf and then 10 quantiles of the t Student distribution
///
/// \macro_image
/// \macro_code
///
/// \author Magdalena Slawinska

#include "TH1.h"
#include "TF1.h"
#include "TCanvas.h"
#include "TSystem.h"
#include "TLegend.h"
#include "TLegendEntry.h"
#include "Math/DistFunc.h"


void tStudent()
{

   /* gSystem->Load("libMathMore");*/

   // this is the way to force load of MathMore in Cling
   ROOT::Math::MathMoreLibrary::Load();

   int n=100;
   double a=-5.;
   double b=5.;
   //double r  = 3;
   TF1* pdf = new TF1("pdf", "ROOT::Math::tdistribution_pdf(x,3.0)", a,b);
   TF1* cum = new TF1("cum", "ROOT::Math::tdistribution_cdf(x,3.0)", a,b);

   TH1D* quant = new TH1D("quant", "", 9, 0, 0.9);

   for(int i=1; i < 10; i++)
      quant->Fill((i-0.5)/10.0, ROOT::Math::tdistribution_quantile((1.0*i)/10, 3.0 ) );

   double xx[10];
   xx[0] = -1.5;
   for(int i=1; i<9; i++)
      xx[i]= quant->GetBinContent(i);
   xx[9] = 1.5;
   TH1D* pdfq[10];
   //int nbin = n/10.0;
   for(int i=0; i < 9; i++) {
      int nbin = n * (xx[i+1]-xx[i])/3.0 + 1.0;
      TString name = "pdf";
      name += i;
      pdfq[i]= new TH1D(name, "", nbin,xx[i],xx[i+1] );
      for(int j=1; j<nbin; j++) {
         double x= j*(xx[i+1]-xx[i])/nbin + xx[i];
         pdfq[i]->SetBinContent(j, ROOT::Math::tdistribution_pdf(x,3));
      }
   }

   TCanvas *Canvas = new TCanvas("DistCanvas", "Student Distribution graphs", 10, 10, 800, 700);
   pdf->SetTitle("Student t distribution function");
   cum->SetTitle("Cumulative for Student t");
   quant->SetTitle("10-quantiles  for Student t");
   Canvas->Divide(2, 2);
   Canvas->cd(1);
   pdf->SetLineWidth(2);
   pdf->DrawCopy();
   Canvas->cd(2);
   cum->SetLineWidth(2);
   cum->SetLineColor(kRed);
   cum->Draw();
   Canvas->cd(3);
   quant->Draw();
   quant->SetLineWidth(2);
   quant->SetLineColor(kBlue);
   quant->SetStats(0);
   Canvas->cd(4);
   pdfq[0]->SetTitle("Student t & its quantiles");
   pdf->SetTitle("");
   pdf->Draw();
   //pdfq[0]->SetAxisRange(-1.5, 0, 1.5,1.0);
   pdfq[0]->SetTitle("Student t & its quantiles");
   for(int i=0; i < 9; i++) {
      pdfq[i]->SetStats(0);
      pdfq[i]->SetFillColor(i+1);
      pdfq[i]->Draw("same");
   }
   Canvas->Modified();
   Canvas->cd();
}
